Accepted Solutions
Hi @Ashya,
Welcome to the community!
I agree that the location is probably a good candidate for a random effect, but I would think plant varieties would be fixed along with treatment. It wouldn't necessarily be wrong to treat variety as random, but it seems a bit odd unless the varieties you tested were selected to be a representative sample of all varieties that you would like to generalize the results to. Having other fixed effects other than treatment does not diminish your ability to compare the efficacy of the treatment across plant varieties.
You can fit the appropriate model several ways in the Fit Model platform if you have JMP Pro. The Mixed Model personality in Fit Model is preferable if you have Pro. If you have just have base JMP, you can specify your model this way:
Again, you can treat variety as random if you really want to. I would definitely not exclude it, because if it does explain a lot of the variance, excluding that term will cause all the variance explained by variety to go into the residual noise, and your test for the treatment effect will by less powerful.
As far as checking assumptions, you'll want to do that based on conditional residuals rather than regular ("marginal") residuals because the marginal residuals don't consider random effects and may cause the diagnostic plots to look like they fail the assumption. To get the conditional residuals without JMP Pro, go to the red-arrow in the report window > Save > Save Conditional Residuals. Then you'll need to plot them in distribution to check normality with a normal quantile plot or Shapiro-Wilk test for goodness-of-fit after fitting a normal distribution to the conditional residuals.
You can similarly plot the conditional residuals on a run chart to check for independence. If you want to create a residual vs. predicted plot, you'll also want to save the conditional predicted values and then construct the plot in something like Graph Builder.
If you do have JMP Pro, you can get all the conditional residual plots within the Fit Model report with the Mixed Models personality, which is really nice.
Hi @Ashya,
Welcome to the community!
I agree that the location is probably a good candidate for a random effect, but I would think plant varieties would be fixed along with treatment. It wouldn't necessarily be wrong to treat variety as random, but it seems a bit odd unless the varieties you tested were selected to be a representative sample of all varieties that you would like to generalize the results to. Having other fixed effects other than treatment does not diminish your ability to compare the efficacy of the treatment across plant varieties.
You can fit the appropriate model several ways in the Fit Model platform if you have JMP Pro. The Mixed Model personality in Fit Model is preferable if you have Pro. If you have just have base JMP, you can specify your model this way:
Again, you can treat variety as random if you really want to. I would definitely not exclude it, because if it does explain a lot of the variance, excluding that term will cause all the variance explained by variety to go into the residual noise, and your test for the treatment effect will by less powerful.
As far as checking assumptions, you'll want to do that based on conditional residuals rather than regular ("marginal") residuals because the marginal residuals don't consider random effects and may cause the diagnostic plots to look like they fail the assumption. To get the conditional residuals without JMP Pro, go to the red-arrow in the report window > Save > Save Conditional Residuals. Then you'll need to plot them in distribution to check normality with a normal quantile plot or Shapiro-Wilk test for goodness-of-fit after fitting a normal distribution to the conditional residuals.
You can similarly plot the conditional residuals on a run chart to check for independence. If you want to create a residual vs. predicted plot, you'll also want to save the conditional predicted values and then construct the plot in something like Graph Builder.
If you do have JMP Pro, you can get all the conditional residual plots within the Fit Model report with the Mixed Models personality, which is really nice.
Sure. So Box-Cox recommends some optimal transformation to make your variance more homogenous and the residuals more normal. Basically, it evaluates the SSE for the model across a range of power transforms (y^λ), except the value λ = 0 indicates a natural log transform. The transform that minimizes the SSE is the "best" transform. However, bottom of the curve is usually kinda flat, so you can choose various transformations within a neighborhood. You usually want to pick one that corresponds to something meaningful. For example, if Best λ = -0.98, I would choose to take the inverse because -0.98 is really close to -1.
Here's an example: I generated a linear model using normal errors and squared all the response values. I should expect Box-Cox to tell me I need to take the square root to have normal data again. Here's what I actually got:
You can see that the "best" transform is 0.451, but I know the real answer is 0.5 and this is really close. If I didn't know the real answer, I would still choose 0.5. You can re-run your model with your desired transform by clicking the red-arrow next to "Box-Cox Transformations" and selecting "Replace with Transform." You'll get a pop-up box that asks you to type in the value you want. Press OK and you'll get a new Fit Model with the transformed response.